信道极化码理论及其量化译码研究

发布时间：2018-03-26 12:13

本文选题：极化码　切入点：高斯近似　出处：《北京邮电大学》2015年硕士论文

【摘要】：自1948年香农提出信道编码理论以来,信道编码界的研究者们沿着香农所指引的方向,向可靠性极限(香农限)逼近。Turbo码和LDPC码在BPSK调制下已经达到了距离香农限不到0.1dB的优异性能。然而,这些结果都是在码长极长的情况下通过仿真得到,并无严格的理论可达性证明。2009年由Erdal Arikan中提出的极化码是第一种被严格证明可以达到信道容量的构造性的信道编码方法,极化码以较低的编译码复杂度及其容量可达性受到学术界的广泛关注。这种新的编码方式可以对编码和调制进行联合优化,不仅可以逼近信道容量,同时可以提高频谱效率。此外由于其结构简单规则,可采用并行译码架构,能进一步提高吞吐效率。极化码以其众多方面的性能和优势有望在未来通信系统中得到重要应用。本文主要关注和研究极化码的实用化译码技术,重点研究AWGN信道下极化码的串行抵消(Successive Cancellation, SC)量化译码算法及相关优化算法。主要包括三个研究点和创新点：首先,在AWGN信道下研究极化码的基本量化译码算法,使其在极化码硬件设计方面更具实用价值和指导意义。本文在高斯近似方法的指导下,提出了基于最小均方误差、最大容量和最大截止速率三种量化准则的SC量化译码算法。其次,在最大截止速率量化准则的基础之上,文中对浮点条件下的高斯近似方法进行改进,使其能够在量化译码条件下对极化码进行构造,并对量化SC译码算法下极化码的误帧率上界进行估计。最后,基于改进高斯近似方法,本文进一步提出SC量化译码下的最优量化比特数搜索算法,压缩不同程度的极化子信道所用的量化比特数,从而降低量化译码的平均量化比特数。此外,本文还从对数概率域和对数似然率域两方面对列表译码算法的量化问题进行阐述和初步研究,并给出了简单可行的量化译码方案。仿真分析表明,在文中提出的三种量化准则下,SC量化译码算法采用6bit均匀量化足以达到浮点译码性能,且改进的高斯近似方法可以准确估计量化SC译码算法的误块率上界,在最优量化比特搜索算法下,平均量化比特数可以降低到4.5bit。而对于列表译码算法的量化,基于对数概率域的量化方法在信道一侧采用4bit量化,逐级增加1bit的量化方式可以达到浮点译码性能。而基于对数似然率的量化译码方法对所有似然率进行7bit的均匀量化即可达到浮点译码性能,该方法更具实用性。
[Abstract]:Since Shannon put forward channel coding theory in 1948, researchers in channel coding field have followed Shannon's direction. Approaching to the reliability limit (Shannon limit). Turbo code and LDPC code have achieved the excellent performance of distance Shannon limit less than 0.1dB under BPSK modulation. However, these results are obtained by simulation under the condition of extremely long code length. The polarimetric code proposed by Erdal Arikan in 2009 is the first channel coding method which is strictly proved that it can achieve channel capacity. Polarization codes have attracted much attention in academia for their low encoding and decoding complexity and their capacity reachability. This new coding scheme can be combined to optimize coding and modulation, and it can not only approximate the channel capacity, but also improve the performance of polarimetric codes. In addition, the parallel decoding architecture can be used to further improve the throughput efficiency because of its simple structure. Polarization codes are expected to be important applications in future communication systems due to their performance and advantages in many aspects. This paper mainly focuses on the practical decoding technology of polarimetric codes, focusing on the serial cancellation of polarimetric codes over AWGN channels and the related optimization algorithms, including three research points and innovations:. First of all, the basic quantization decoding algorithm of polarization code is studied in AWGN channel, which makes it more practical and instructive in the design of polarization code hardware. Under the guidance of Gao Si's approximation method, this paper proposes a new algorithm based on minimum mean square error (MMSE). SC quantization decoding algorithm for maximum capacity and maximum cut-off rate quantization criterion. Secondly, on the basis of the maximum cut-off rate quantization criterion, the Gao Si approximation method under floating point condition is improved in this paper. It can construct the polarization code under the condition of quantization decoding, and estimate the upper bound of the frame error rate of the polarization code under the quantization SC decoding algorithm. Finally, based on the improved Gao Si approximation method, In this paper, we further propose an optimal quantization bit number search algorithm for SC quantization decoding, which compresses the quantized bits used in different polarization subchannels, thus reducing the average quantization bit number of quantization decoding. In this paper, the quantization problem of list decoding algorithm is discussed and studied from two aspects of logarithmic probability domain and logarithmic likelihood rate domain, and a simple and feasible quantization decoding scheme is given. Simulation results show that 6bit uniform quantization is sufficient to achieve floating-point decoding performance under the three quantization criteria proposed in this paper, and the improved Gao Si approximation method can accurately estimate the upper bound of block error rate of quantization SC decoding algorithm. Under the optimal quantization bit search algorithm, the average quantized bit number can be reduced to 4.5 bits.For the quantization of list decoding algorithm, the quantization method based on logarithmic probability domain uses 4bit quantization on the channel side. The performance of floating-point decoding can be achieved by incrementing the quantization of 1bit step by step, while the uniform quantization of all likelihood rates by quantization based on logarithmic likelihood can achieve the performance of floating-point decoding, which is more practical.
【学位授予单位】：北京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN911.22

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